In a covered medium saucepan cook broccoli in a small amount of boiling salted water about 10 minutes or until tender. Drain well, reserving cooking liquid.
In a small skillet cook onion in hot oil for 8 to 10 minutes or until onion is tender. In a food processor or blender combine broccoli, onion mixture, Parmesan cheese, and crushed red pepper. Cover and process or blend until nearly smooth. If mixture seems dry and thick, stir in enough of the reserved cooking liquid, 1 tablespoon at a time, to make a spreading consistency. Cover and chill for at least 3 hours or up to 24 hours.
Serve with vegetable dippers, baked tortilla wedges, or assorted crackers. Makes 1 cup spread.